{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3d0ef82b",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Replication file for 'The Intertemporal Keynesian Cross'\n",
    "### Alternative ways of solving the IKC (appendix Figure A.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b824939",
   "metadata": {},
   "source": [
    "Adrien Auclert, Matt Rognlie, Ludwig Straub\n",
    "\n",
    "April 2024"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b729f3a6",
   "metadata": {},
   "source": [
    "Import main packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a7ce81e5",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np  \n",
    "import matplotlib.pyplot as plt \n",
    "import json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0e1d69c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sec34_plots import set_texfig\n",
    "import calibration\n",
    "import models_heterogeneous, models_analytical\n",
    "import jacobian_manipulation as jac"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb799fa9",
   "metadata": {},
   "source": [
    "# Preliminaries: model and shock\n",
    "Load the HA-one model and calibration, also calculating $\\mathbf{A}$ and $\\mathbf{M}$ Jacobians, as in `main_sec5.ipynb`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c9330076",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('solved_params.json', 'r') as f:\n",
    "    params = json.load(f)\n",
    "\n",
    "calib_ha_one, _ = calibration.get_ha_calibrations()\n",
    "ha_one = models_heterogeneous.ha_one\n",
    "ss = ha_one.steady_state({**calib_ha_one, **params['HA-one']})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "29bbb7bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 300\n",
    "r = calibration.r\n",
    "J = ha_one.jacobian(ss, ['Z'], ['C', 'A'], T=T)\n",
    "M, A = J['C', 'Z'], J['A', 'Z']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b7faacf",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now specify our fiscal shock of interest, which for this example we'll choose to have $\\rho_G=0.8$ and $\\rho_B=0.5$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "34a59c9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from aux_fiscal import Bplan, Tplan\n",
    "\n",
    "dG = 0.8**np.arange(T)\n",
    "dB = Bplan(dG, 0.5)\n",
    "dT = Tplan(dG, dB, 1+r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "385ea44d",
   "metadata": {},
   "source": [
    "# Alternative solution methods\n",
    "### Approach 1: calculate multiplier $\\mathcal{M}$\n",
    "This approach directly implements the solution $d\\mathbf{Y} = \\mathcal{M} (d\\mathbf{G} - \\mathbf{M}d\\mathbf{T})$ from proposition 2, where $\\mathcal{M} \\equiv (\\mathbf{K}(\\mathbf{I}-\\mathbf{M}))^{-1}\\mathbf{K} = \\mathbf{A}^{-1}\\mathbf{K}$ and $\\mathbf{K} \\equiv -\\sum_{t=1}^\\infty (1+r)^{-t}\\mathbf{F}^t$. We use it as our primary approach in `main_sec5.ipynb`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "645365e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "K = jac.Kmat(r, T)\n",
    "curlyM = np.linalg.solve(A, K)\n",
    "dY_1 = curlyM @ (dG - M @ dT)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad848419",
   "metadata": {},
   "source": [
    "### Approach 2: asset Jacobian\n",
    "This approach directly solves via the lineared asset-market clearing relation $\\mathbf{A}(d\\mathbf{Y}-d\\mathbf{T}) = d\\mathbf{B}$, giving $d\\mathbf{Y} = \\mathbf{A}^{-1}d\\mathbf{B} + d\\mathbf{T}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6c4cbe95",
   "metadata": {},
   "outputs": [],
   "source": [
    "dY_2 = np.linalg.solve(A, dB) + dT"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f66a077",
   "metadata": {},
   "source": [
    "As discussed in the appendix, it is easy to demonstrate equivalence here to the first approach. ADD MORE CONTENT HERE. We see that the two are numerically quite close:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9462ba96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.962579401914581e-10"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(dY_1 - dY_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42ddce94",
   "metadata": {},
   "source": [
    "### Approach 3: naively solving the Intertemporal Keynesian Cross\n",
    "Alternatively, we can write the intertemporal Keynesian cross $d\\mathbf{Y} = d\\mathbf{G}-\\mathbf{M}d\\mathbf{T} + \\mathbf{M}d\\mathbf{Y}$ and naively try to obtain a solution $d\\mathbf{Y} = (\\mathbf{I}-\\mathbf{M})^{-1}(d\\mathbf{G}-\\mathbf{M}d\\mathbf{T})$, ignoring the fact that the actual infinite-dimensional operator $\\mathbf{I}-\\mathbf{M}$ is not invertible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "af2a669a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dY_3 = np.linalg.solve(np.eye(T) - M, dG - M @ dT)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40452008",
   "metadata": {},
   "source": [
    "This delivers roughly the right solution, but the gap with the previous approaches is around $10^{-3}$ (vs. under $10^{-9}$ between the first two approaches):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9b1a887b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0009049304253809859"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(dY_1 - dY_3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1cf9755",
   "metadata": {},
   "source": [
    "It is only possible to implement this approach in the first place because when truncated, $\\mathbf{I}-\\mathbf{M}$ is not quite singular; but, since it is *close* to being singular, the error tends to be quite large. We see this below with the smallest singular value being around $10^{-8}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "81a923f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.53611897e-02, 1.92337930e-02, 1.45487970e-02, 1.15168014e-02,\n",
       "       1.24849831e-08])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.svd(np.eye(T) - M)[1][-5:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbff6a9b",
   "metadata": {},
   "source": [
    "### Approach 4: rounds of a keynesian cross\n",
    "Here, we try a very different approach, which is to attempt to iteratively solve the Intertemporal Keynesian Cross by repeatedly applying $d\\mathbf{Y}^{(k)} = d\\mathbf{G} - \\mathbf{M}d\\mathbf{T} + \\mathbf{M}d\\mathbf{Y}^{(k-1)}$, by analogy with the traditional idea of iteratively applying the static Keynesian cross."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "522513be",
   "metadata": {},
   "outputs": [],
   "source": [
    "dY_pe = dG - M @ dT # partial equilibrium impulse\n",
    "dYk = np.zeros_like(dY_pe) # initialize dY^0 = 0\n",
    "save = np.empty((10, len(dY_pe))) # save every 500 impulse responses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "de1c38f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10000):\n",
    "    if i % 500 == 0 and i < 5000:\n",
    "        plt.plot(dYk, label=f'round {i}')\n",
    "        save[i // 500,:] = dYk\n",
    "    dYk = dY_pe + M @ dYk\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d912afef",
   "metadata": {},
   "source": [
    "We see that this computation converges to some $d\\mathbf{Y}^\\infty$ that is clearly not a solution. Interestingly, however, it turns out that $d\\mathbf{Y}$ differs from $d\\mathbf{Y}^\\infty$ by a constant multiple $d\\lambda$ of the eigenvector $\\mathbf{v}$ corresponding to the highest eigenvalue of $\\mathbf{M}$.\n",
    "\n",
    "We identify this $\\mathbf{v}$ and calculate $d\\lambda$ to enforce that $dY_{T-1} = 0$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0ea99b2c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max eigenvalue = 0.9999927869324664\n"
     ]
    }
   ],
   "source": [
    "w, v = np.linalg.eig(M)\n",
    "i = np.argmax(w)\n",
    "print('Max eigenvalue =', w[i].real)\n",
    "mvec = v[:,0].real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "79c2a6e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "dlambda = - dYk[-1] / mvec[-1]\n",
    "dY_4 = dYk + dlambda * mvec"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bb68253",
   "metadata": {},
   "source": [
    "This process gives us a solution that is close to being correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e1808069",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.62025917361098e-07"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(dY_4 - dY_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ff4e3e",
   "metadata": {},
   "source": [
    "Incidentally, sometimes this iterative process converges directly to the correct solution, with no eigenvector correction required. This is the case for our BU or TABU models, as we see below for TABU—although again convergence is slow enough that thousands of iterations are required to get an exact solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "682570d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.547593962115691e-11"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ms, As = models_analytical.MA_all(params, r, T)\n",
    "\n",
    "# true TABU solution\n",
    "dY_tabu = np.linalg.solve(As['TABU'], dB) + dT\n",
    "\n",
    "# iterative TABU solution\n",
    "dY_pe = dG - Ms['TABU'] @ dT # partial equilibrium impulse\n",
    "dYk = np.zeros_like(dY_pe) # initialize dY^0 = 0\n",
    "\n",
    "for i in range(10000):\n",
    "    dYk = dY_pe + Ms['TABU'] @ dYk\n",
    "    dYk[200:] = 0 # approximately zero after 200 periods, avoids truncation-related issues\n",
    "\n",
    "np.max(np.abs(dYk - dY_tabu))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b73b33ed",
   "metadata": {},
   "source": [
    "The key difference between our HA-one model, where the result of iteration needs to be corrected for the eigenvector, and a model like TABU where it does not, is discussed in footnote A-14 in the paper. In general, the operator $\\tilde{\\mathbf{M}}$ defined by $\\tilde{M}_{ts}=(1+r)^{-(t-s)}M_{ts}$ is column-stochastic and can be interpreted as specifying a Markov chain over the natural numbers, giving the odds that a present-value dollar made in period $s$ will be spent in period $t$. \n",
    "\n",
    "When this Markov chain is transient, then it has no stationary measure, and the iterative process above converges. When it is recurrent, however, it does have a stationary measure, which corresponds to indeterminacy of the IKC in bounded *present-value* sequences, i.e. there is some $d\\mathbf{Y}$ such that $(1+r)^{-t}dY_t$ is bounded and that $\\mathbf{M}d\\mathbf{Y}=d\\mathbf{Y}$. The IKC may be determinate in the current-value sense (i.e. there is still only one solution that is actually bounded), but the iterative process will generally pick up some multiple of the stationary measure $d\\mathbf{Y}$ in addition to the unique current-value-bounded solution. This $d\\mathbf{Y}$ is distorted due to truncation, but we can still pick it up by looking at which eigenvalue is close to 1.\n",
    "\n",
    "We can test for transience vs. recurrence by seeing whether applying the asymptotic column of $\\tilde{\\mathbf{M}}$ (the \"symbol\") causes on average an increase or decrease in the time period—i.e. whether well-anticipated income is spent, on average, in earlier or later periods than it is received."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3ec41ca2",
   "metadata": {},
   "outputs": [],
   "source": [
    "m_ha_one = np.concatenate((M[:, -1], M[-1, :-1][::-1]))\n",
    "m_tabu = np.concatenate((Ms['TABU'][:, -1], Ms['TABU'][-1, :-1][::-1]))\n",
    "ts = np.arange(2*T-1) - (T-1)   # time indices from -(T-1) through T-1\n",
    "mtilde_ha_one = m_ha_one * (1+r)**(-ts)\n",
    "mtilde_tabu = m_tabu * (1+r)**(-ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8d76058",
   "metadata": {},
   "source": [
    "On average, well-anticipated income is spent before it is received in our HA-one model, so that it is recurrent (explaining the difficulty in applying the iteration above):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "22a113f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.140744654743851"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mtilde_ha_one @ ts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd41b266",
   "metadata": {},
   "source": [
    "It is spent after it is received in our TABU model, so that it is transient (explaining why the iteration works without any adjustment):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b3d5818b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2085605330676006"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mtilde_tabu @ ts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f5c8d44",
   "metadata": {},
   "source": [
    "### Approach 5: deleting the first row of the IKC\n",
    "We premultiply by $\\mathbf{K}$ when formulating our solution in proposition 2 because this gives us back the asset market clearing condition, which we know to be consistent with equilibrium.\n",
    "\n",
    "In cases where our model has quasi-Toeplitz form, however, and we can apply the winding number criterion for invertibility, the significant fact about $\\mathbf{K}$ is that it has a winding number of -1, so that when we compose it with $\\mathbf{I}-\\mathbf{M}$, which has a winding number of 1, the resulting $\\mathbf{K}(\\mathbf{I}-\\mathbf{M})$ will have winding number 0 and genericaly be invertible.\n",
    "\n",
    "In this case, we could replace $\\mathbf{K}$ with another operator that has winding number of -1. The simplest choice is arguably $\\mathbf{F}$, the forward operator. Premultiplying a sequence-space equation by the forward operator is tantamount to removing the first row of the equation.\n",
    "\n",
    "Implementing this, we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b79a6ab1",
   "metadata": {},
   "outputs": [],
   "source": [
    "I_M = np.eye(T) - M\n",
    "dY_pe = dG - M @ dT\n",
    "dY_5 = np.linalg.solve(I_M[1:, :-1], dY_pe[1:]) # delete first row and last column"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16538c74",
   "metadata": {},
   "source": [
    "This turns out to be extremely accurate, comparable to the first two approaches:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "924f330b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.601206496512305e-10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(np.abs(dY_5 - dY_1[:-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a13ffc1e",
   "metadata": {},
   "source": [
    "# Figure A.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cadbb06",
   "metadata": {},
   "source": [
    "#### Figure A.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6fd62f30",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Tplot = 11\n",
    "style_list = ['solid',  'dashed', 'dashdot', 'dotted']\n",
    "    \n",
    "set_texfig(fontsize=15)\n",
    "\n",
    "plt.figure(figsize =(6, 4.5))\n",
    "plt.plot(dY_2[0:Tplot][0:Tplot], color='blue', linestyle=style_list[0], label='Asset Jacobian solution', linewidth=2.5)\n",
    "plt.plot(dY_3[0:Tplot], color='blue', linestyle=style_list[1], label='Direct IKC solution', linewidth=2.5)\n",
    "plt.plot(dY_1[0:Tplot], color='blue', linestyle=style_list[2], label=r'Solution using $\\mathcal{M}$', linewidth=2.5)\n",
    "plt.plot(dY_4[0:Tplot], color='blue', linestyle=style_list[3], label='Iterated IKC rounds', linewidth=2.5)\n",
    "plt.xlabel(r'Year $t$')\n",
    "plt.ylabel(r'\\% of $Y_{ss}$')\n",
    "plt.legend(framealpha=0)\n",
    "plt.title(r'(a) Output effect $d\\mathbf{Y}$', x=0.5, y=1.02)\n",
    "plt.savefig('figures/figA1_a.pdf', format='pdf', transparent=True, bbox_inches = \"tight\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize =(6, 4.5))\n",
    "for k in range(10):\n",
    "    plt.plot(save[k,:], label=r'$k='+str(500*k)+'$', linewidth=2.5)\n",
    "plt.xlabel(r'Year $t$')\n",
    "plt.legend(framealpha=0, loc='lower left')\n",
    "plt.ylim(-200,5)\n",
    "plt.title(r'(b) Iterated rounds $dY_0^{k}$', x=0.5, y=1.02)\n",
    "plt.savefig('figures/figA1_b.pdf', format='pdf', transparent=True, bbox_inches = \"tight\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize =(6, 4.5))\n",
    "plt.plot(mvec, color='blue', linewidth=2.5, label=r'$\\mathbf{v}$')\n",
    "plt.xlabel(r'Year $t$')\n",
    "plt.title(r'(c) Eigenvector $\\mathbf{v}$', x=0.5, y=1.02)\n",
    "plt.savefig('figures/figA1_c.pdf', format='pdf', transparent=True, bbox_inches = \"tight\")\n",
    "plt.show()\n"
   ]
  }
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